A ____________ has no dimension and is represented by a small dot.

Answer:

D -5/12

Step-by-step explanation:

2 1/2 = 2·(2/2) + 1/2 = 5/2

Dividing by 6 is the same as multiplying by 1/6.

... (-5/2)×(1/6) = -5·1/(2·6) = -5/12

Answer:

Mean score for the students = 593.3

Step-by-step explanation:

Name    Score

Julia      650

Andrew 550

Jason    380

Cathy     720

Jessica   710

Robert    550

1) Mean Score = [tex]\frac{Sum of the scores}{Total number of students}[/tex]

= [tex]\frac{650+550+380+720+710+550}{6}[/tex]

= 593.33

2) Upon rounding off to the nearest tenth, we get

Mean Score = 593.3 (since the hundredth digit is lesser than 5, the tenth digit is not increased)

Answer:

593.3

Step-by-step explanation:

Assuming random sample, assuming "point estimate of mean score" means "estimate of mean score in points",

(650+550+380+720+710+550)/6 is 593.3

Sample size 6 population size 25 is irrelevant except to note estimate might not be very good.

Answer:

$3.46

Step-by-step explanation:

Unpaid February balance = $345.67

Annual Percentage Rate(APR) = 13.99 %

                                                  = [tex]\frac{13.99}{100}[/tex]

                                                  = 0.1399 (converted into decimal)

Periodic (monthly) interest rate = [tex]\frac{0.1399}{12}[/tex]  (since there are 12 months in a year)

                                                    = 0.01

Interest he owes on his unpaid February balance of $345.67

       = Periodic (monthly) interest rate * unpaid February balance

       = 0.01 * 345.67

       = 3.456

       = $3.46     (rounded off to the hundredth place)

Answer:

a) [tex]-5x^{2}+3x+27[/tex]

b) [tex]-5x^{2}+3x+9[/tex]

Step-by-step explanation:

a) Let the required polynomial be p(x).

We have the relation, [tex]5x^{2}-3x-9[/tex] + p(x) = 18

i.e. p(x) = 18 [tex]-5x^{2}+3x+9[/tex]

i.e. p(x) = [tex]-5x^{2}+3x+27[/tex]

b) Let the required polynomial be q(x).

We have the relation, [tex]5x^{2}-3x-9[/tex] + q(x) = 0

i.e. q(x) = 0 [tex]-5x^{2}+3x+9[/tex]

i.e. q(x) = [tex]-5x^{2}+3x+9[/tex]

Answer:

(a) [tex]-5x^2+3x+27[/tex]

(b)  [tex]-5x^2+3x+9[/tex]

Step-by-step explanation:

(a)

Let the polynomial be Q(x).

Given polynomial P(x) = [tex]5x^2-3x-9[/tex]

As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 18.

[tex]P(x)+Q(x) = 18[/tex]

[tex]5x^2-3x-9 +Q(x) = 18[/tex]

⇒[tex]Q(x) = 18 -(5x^2-3x-9)[/tex]

or

[tex]Q(x) = 18 -5x^2+3x+9[/tex]

Simplify:

[tex]Q(x) =-5x^2+3x+27[/tex]

Therefore, the polynomial is,  [tex]-5x^2+3x+27[/tex]

Check:

[tex]P(x)+Q(x)[/tex] = [tex]5x^2-3x-9 +(-5x^2+3x+27)[/tex]

                      = [tex]5x^2-3x-9 -5x^2 +3x+27[/tex]

                       = 18

(b)

Let the polynomial be Q(x).

Given polynomial P(x) = [tex]5x^2-3x-9[/tex]

As per the given statement: A polynomial(Q(x)) which, when added to the polynomial [tex]5x^2-3x-9[/tex], is equivalent to 0.

[tex]P(x)+Q(x) = 0[/tex]

[tex]P(x) = -Q(x)[/tex]

⇒[tex]Q(x) = -(5x^2-3x-9)[/tex]

or

[tex]Q(x) = -5x^2+3x+9[/tex]

Therefore, the polynomial is,  [tex]-5x^2+3x+9[/tex]

Check:

[tex]P(x)+Q(x)[/tex]=[tex]5x^2-3x-9 +(-5x^2+3x+9)[/tex]

                      = [tex]5x^2-3x-9-5x^2 +3x+9[/tex]

                       = 0

The equation 15x + 8y = 56 can be rewritten in slope-intercept form (y = mx + b) as y = -15/8x + 7, where -15/8 is the slope and 7 is the y-intercept.

To convert the equation 15x + 8y = 56 into slope-intercept form (y = mx + b), we want to isolate y. Here are the steps:

In this equation, -15/8 is the slope, and 7 is the y-intercept. This means the line intersects the y-axis at y = 7, and for every 8 units increase in x, there is a 15 unit decrease in y, as the slope is negative.

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Answer:

4^x+1

Step-by-step explanation:

because i got it wrong

Answer:

[tex]y= 4^{x+1}[/tex]

Step-by-step explanation:

Answer:

24 gallons

Step-by-step explanation:

18 divided by 3 is 6

6 x 4 = 24

so there are 24 gallons as a whole

You said . . . . . 18 = 3/4 g

Multiply each side by 4 . . . 72 = 3g

Divide each side by 3 . . . 24 = g

36 cm

Let s represent the side of the square in cm. Then s+3 and s-2 are the sides of the rectangle of interest.

The area of the rectangle is the product of its side lengths:

... rectange area = (s+3)(s-2) = s² +s -6

The area of the square is the product of its side lengths, both of which are s.

... square area = s²

The difference of these areas is 30 cm², so ...

... rectangle area - square area = 30

... (s² +s -6) -(s²) = 30

... s = 36 . . . . . . . . . . . . simplify, add 6

The side of the square is 36 cm.

_____

Check

The rectangle dimensions are 39 cm by 34 cm, so its area is

... (39 × 34) cm² = 1326 cm²

The area of the square is (36 cm)² = 1296 cm²

The difference in areas is (1326 -1296) cm² = 30 cm², as required.

Answer:

[tex]<\:3[/tex] is the angle of elevation from the boat to the lighthouse.

Step-by-step explanation:

From the boat, the angle through which you will raise your head to see the light house is the angle of elevation, which is [tex]<\:3[/tex].

See graph for the illustration.

The correct answer is A

Answer:

The angle of elevation from the boat to the lighthouse is:

First option: <3

Step-by-step explanation:

The angle of elevation from the boat to the lighthouse is the angle of the visual since the boat to the lighthouse with the horizontal, according with the graph this angle is <3 (First option)

Answer:

(x, y) = (5, 1)

Step-by-step explanation:

To eliminate x, you can double the second equation and subtract the first.

... 2(x +4y) -(2x -3y) = 2(9) -(7)

...11y = 11 . . . . . simplify

... y = 1 . . . . . . divide by 11

Using the second equation to find x, we have ...

... x + 4·1 = 9

... x = 5 . . . . . subtract 4

_____

Check

2·5 -3·1 = 10 -3 = 7 . . . . agrees with the first equation

(Since we used the second equation to find x, we know it will check.)

Answer:

$51

Step-by-step explanation:

To solve this, we must divide the total amount of miles by the miles per gallon, and multiply that by the cost per gallon.

430 / 26 = 16.53

Because this is talking about gallons, we should round up to 17.

17 * 3 = 51

It costs $51 to drive 430 miles when gasoline costs $3 per gallon.

Answer:

$49.62

Step-by-step explanation:

We know that the car travels for 26 miles in 1 gallon. So we will find out the number of gallons it requires to travel for 430 miles by simple ratio method.

[tex]\frac{1 gallon}{x} =\frac{26 miles}{430}[/tex]

[tex]x=\frac{430}{26}[/tex]

[tex]x=16.54[/tex]

Now that we know that the car needs 16.54 gallons of gasoline to drive for 430 miles, we can simply multiply the number of gallons by the cost per gallon to find its total cost.

Total cost of gasoline to drive 430 miles = 16.54 x 3 = $49.62

Answer:

Step-by-step explanation:

riders : walkers = 10 : 1

The ratio tells you that 10 students ride the bus for every 1 student that walks. Since 10 is more than 1, more students ride the bus.

We know more students are riders, because we know that 10 is more than 1.

Answer:

B) 6

Step-by-step explanation:

It is 45, 45, 90 degrees right triangle, the ratio of the triangle 1:1:√2

Hypotenuse = 3√2*√2

= 3*2

= 6

Thank you.

Answer:

6

Step-by-step explanation:

Hypotenuse is the side that is opposite of the 90 degree angle (the longest side as well).

As seen in the triangle, the side opposite of 45° angle is known AND we want to find the hypotenuse.

Which trigonometric ratio relates opposite with hypotenuse?

SINE

We can write:

[tex]sin(A)=\frac{opposite}{hypotenuse}\\sin(45)=\frac{3\sqrt{2}}{h}[/tex]

We let hypotenuse be [tex]h[/tex]. Also we know that [tex]sin(45)=\frac{1}{\sqrt{2}}[/tex]

Now we can solve for [tex]h[/tex]:

[tex]sin(45)=\frac{3\sqrt{2}}{h}\\h*sin(45)=3\sqrt{2}\\h=\frac{3\sqrt{2}}{sin(45)}\\h=\frac{3\sqrt{2}}{\frac{1}{\sqrt{2}}}\\h=3\sqrt{2}*\frac{\sqrt{2}}{1}\\h=6[/tex]

(we used the identity [tex](\sqrt{a})(\sqrt{a})=a[/tex])

2nd answer choice is right. Hypotenuse is 6.

Answer:

7x^2y(x +2xy^2 -y)

Step-by-step explanation:

7, x^2, and y are factors of every term, so we can start by factoring those out.

... = 7x^2y(x +2xy^2 -y)

The trinomial does not factor further, so this is it.

Answer:

7x^2y(x +2xy^2 -y)

Step-by-step explanation:

7x^3y +14x^2y^3 − 7x^2y^2

WE find out GCF

7x^3y= 7*x*x*x*y

14x^2y^3= 7*2*x*x*y*y*y

7x^2y^2 = 7 *x*x*y*y

GCF is 7x^2y

Factor out GCF from the given expression. when we factor out 7x^2y we divide each term by GCF. we put GCF 7x^2y outside

7x^2y(x +2xy^2 -y)

x² + y² = 50

The circle centered at (h, k) with radius r has equation ...

... (x -h)² + (y -k)² = r²

You have (h, k) = (0, 0), so all we need to do is find r². We can do that by choosing r² so that the equation is true at the given point.

... x² + y² = (5)² + (-5)² = 25 + 25 = 50

Your equation is x² + y² = 50.

Answer:

The measure of angle B is positive

Step-by-step explanation:

we know that

Positive angles are those measured counterclockwise.

therefore

in this problem

The measure of angle B is positive

Answer:

D) 15

Step-by-step explanation:

We know the formula for direct variation is

y=kx

Substituting y=5 and x=4 we can calculate k

5=k4

Divide each side by 4

5/4 =k

Now y= 5/4 x

If x =12

y =5/4*12

y = 15

Answer:

The correct option is A. The height of tree is 60 ft.

Step-by-step explanation:

From the given figure it is noticed that the building is creating a right angle triangle from a point and the tree divides the hypotenuse and base in two equal part.

According to midpoint theorem of triangle: In a triangle, if a line segment connecting the midpoints of two sides, then the line is parallel to third side. The length of line segment is half of the length of third side.

Using midpoint theorem of triangle, we can say that the length of tree is half of the building.

[tex]Tree=\frac{1}{2}\times Building[/tex]

[tex]Tree=\frac{1}{2}\times 120[/tex]

[tex]Tree=60[/tex]

Therefore correct option is A. The height of tree is 60 ft.

[tex]\bf \textit{exponential form of a logarithm} \\\\ log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=\log_4(0.25) ~\hfill 0.\underline{25}\implies \cfrac{025}{1\underline{00}}\implies \cfrac{1}{4}\implies 4^{-1} \\\\\\ y=\log_4\left( 4^{-1} \right)\implies 4^y=4^{-1}\implies y=-1[/tex]

Answer:

Show ΔBCD ≅ ΔGFE, so ∠C ≅ ∠F. Base angle of an isosceles triangle are congruent, so ΔACF is isosceles.

Step-by-step explanation:

Informally, subtract DE from CE and DF. This will show CD ≅ EF.

Then ΔBCD ≅ ΔGFE by the HL theorem for right triangles.

Corresponding parts of congruent triangles are congruent, namely the angles C and F.

Since base angles of ΔACF are congruent, it is isosceles.

B. mx−y=−b

Start with ...

... y = mx +b

Subtract mx.

... -mx +y = b

You want the leading coefficient positive, so multiply by -1.

... mx -y = -b . . . . matches selection B

Answer: B. mx−y=−b

Step-by-step explanation:

The equation of a line in standard form is given by :-

[tex]Ax+By=C[/tex]

, where A is a positive integer , B and C are integers.

The given equation : [tex]y = mx + b[/tex]

, where m is a positive integer.

The convert it into standard form , we subtract y and b from both sides , we get

[tex]y -y-b= mx + b-y-b[/tex]

Simplify,

[tex]-b= mx -y[/tex]

Or we can write it as [tex] mx -y=-b[/tex] → Standard form.

Thus , the equation of line in standard form = [tex] mx -y=-b[/tex] , where m is a positive integer.

Hence, the correct answer is B. mx−y=−b

Answer:

132(X) + 64(2X) = $1040.00

Step-by-step explanation:

equations

solution

a. It usually works well to let a variable represent the quantity the problem statement is asking you to find. I like to choose variable names that help me remember what the variable stands for. (x and y rarely do that) So, let's choose "a" for the cost of an adult ticket, and "s" for the cost of a student ticket.

The equations express the relationships described by the problem statement. The first relationship expresses the total revenue in terms of the numbers of tickets sold. You know that multiplying the number of tickets by the cost of the ticket will give the revenue from sales of that ticket. So, the total revenue is ...

... 64a +132s = 1040

The problem statement also tells you the relationship between the costs. An adult ticket is twice the cost of a student ticket, so ...

... a = 2s

These equations are your system of linear equations.

_____

b. The solution can be found using substitution. Since the second equation gives an expression for "a", we can use that in the first equation.

... 64(2s) +132s = 1040

... 260s = 1040 . . . . . . . . simplify

... 1040/260 = s = 4

... a = 2s = 2·4 = 8

An adult ticket costs $8; a student ticket costs $4.

Answer:

HL

Step-by-step explanation:

The two hypotenuses of these right triangles are marked congruent, and the leg QS is shared, hence congruent.

The HL theorem applies.

2.54 cm/in

In this context, "constant of proportionality" and "unit rate" mean the same thing.

Answer:

6/x weeks

Hope this helps

Answer:

6/x weeks

Step-by-step explanation:

This is the correct answer, credits to the other person who answered.

64

If each side length is multiplied by 8, the product of two side lengths will be multiplied by 8×8 = 64.

Area is proportional to the product of two side lengths, so will be multiplied by 64.

Answer:

5² - n  

Step-by-step explanation:

Five squared  = 5²

                     n =        n     Subtract n from 5²

                 Diff. = 5² - n

We indicate "taking the difference" by a "minus" sign, so all the other options are wrong.

Answer:

5² - n

Step-by-step explanation:

Five squared is written as = 5²

The symbol of n is n.

The term difference is subtraction.

The difference of five squared and n ⇒ 5² - n

Answer:

none of the above

Step-by-step explanation:

The grocer's revenue will be the product of the number of loaves sold (30-2x) and their price (2.50+0.50x).

Revenue will be positive for values of x between those that make these factors be zero. The number of loaves sold will be zero when ...

... 30 -2x = 0

... 15 -x = 0 . . . . . divide by 2

... x = 15 . . . . . . . add x

The price of each loaf will be zero when ...

... 2.50 +0.50x = 0

... 5 + x = 0 . . . . . . . multiply by 2

... x = -5 . . . . . . . . . . subtract 5

Revenue will be positive for any number of increases greater than -5 and less than 15.

_____

D is the best of the offered choices, but it is incorrect in detail. -5 is a number less than 15, but will give zero revenue.